A problem of terminology

C (known on Million Moments as Inexperienced Mom) works for about 6 hours a week at an after-school tutoring center. My work is flexible such that I'm able to leave early the two days a week that C works. I come home so she can go to work.

The other day, while C was at work, my mom called.

"Oh, you're home already, huh?" she asked.

"Yeah. C starts work at 4, so I have to be home in time for her to go" I replied.

"Well, your work sure is good to let you come home to babysit twice a week."

"Yes, they are."

Ok, we'll stop the conversation there. I have a problem with that terminology. The way I look at it, it's not called "babysitting" when you are taking care of your own kid. Really--I'm the dad. I can take care of my own kid. So I can't feed him by myself; that doesn't make me incompetent in other areas.

I didn't turn like this on my poor mother, who I'm sure doesn't see me as "just a babysitter." But after the conversation was over, I thought about that word, and I realized it just isn't a good fit for what I was doing, but I couldn't think of a better one to use in its place.

After all, the term "babysitting" sounds like it is something that isn't normally my responsibility, and then my responsibility ends when the Mom gets home. My mother isn't the first one to use that term, and I'm sure she won't be the last. So I've got to find a better word to use instead.

What is a good term to use? Primary caregiver? That term has some of the same problems. Any suggestions on how I should handle it when people talk about me "babysitting" my own kid?